before offering "extra security , or prepaid rent"...check with your state's tenant/landlord laws, as in NJ, for example, there is a cap on the maximum amount the landlord can collect, in advance, as a deposit.
Perhaps a CA agent will address that issue.
What they will want to see is proof you have paid your rent on time for the past year (cancelled checks or letter from current landlord), and inome/job verification (you need to show that you CAN afford to pay the rent).
It would also be helpful if you have good reasons for the "not so great" credit score....and you are willing to share your reasons with the landlord.
In this economy, you are not alone - there are others whose credit has suffered, for a variety of reasons, too. Landlords can be more forgiving and flexible under these circumstances.
Best of Luck!